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3 years ago

Find the exact circumference of a circle with an approximate area of 78.5 square feet.

Mathematics

1 answer:

Tresset [83]3 years ago

3 0

Answer:

31.41ft

Step-by-step explanation:

the area A of a circle is πr² = 78.5 square feet

3.1416* r² = 78.5

r² =78.5/3.1416 = 24.987

r = √24.987 = 4.999ft

the circumference C of a circle is 2πr

C = 2* 3.1416 * 4.999 = 31.41ft

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A DJ has a total of 1075 dance, rock,and country songs on her system.The dance selection is three times the size of the rock sel

igor_vitrenko [27]

Dance (D) + Rap (R) + Country (C) = 1,075 songs
D = 3R
C = R + 105

RAP
Subtract 105 from both side:
(3R) + R + (R + 105) = 1,075
-105 -105

Combine all R's:
(3R) + R + R = 970
5R = 970

Divide both sides by 5:
5R = 970
/5 /5
R = 194

DANCE
D = 3(R)
D = 3(194)
D = 582

COUNTRY
C = R + 105
C = 194 + 105
C = 299

So, the DJ has a total of 194 rap songs, 582 dance songs, and 299 country songs.

6 0

4 years ago

drako found an emarald in a cave at a depth between negative 1\2 and negative 1 2\3 meters. Which number could represent the dep

Delvig [45]

Answer:

$(-\frac{7}{6} )$

Step-by-step explanation:

From the question the emerald was located at a depth which is between -1/2 and -1 2/3 meters

This statement can be written as

$(-1\frac{2}{3}) -(-\frac{1}{2} )$

To get the depth, you find the depth of the emerald location, you find difference between the two mentioned depths

$-(1\frac{2}{3} )-(-\frac{1}{2} )\\\\$

Change first term to improper fraction

$=-(\frac{5}{3} )-(-\frac{1}{2} )\\\\$

Find the LCM to solve the operation the involves the fractions.The Least common multiple here is 6 i.e 3*2

$=(-\frac{5}{3} )-(-\frac{1}{2})\\$

$=\frac{-5}{3} +\frac{1}{2} =\frac{-10+3}{6} =\frac{-7}{6}$

The number that could represent the depth at which the emerald was located is

$=\frac{-7}{6}$

6 0

4 years ago

Write the ratio 1/9 4/5 in simplest from

ale4655 [162]

1: 7.2 cant get a whole number

5 0

3 years ago

Angle WXY underwent a sequence of two rotations around different centers. The original size of WXY is 82°. what is the size of t

STatiana [176]

Given:

$\angle WXY=82^\circ$

It underwent a sequence of two rotations around different centers.

To find:

The size of the angle WXY after the sequence of rotations.

Solution:

We know that, rotation is a rigid transformation. It means, the size and shape of the figure remains the same after the rotations. It other words, the figure and its image are congruent after rotation.

So, the measure of angle WXY remains same after the sequence of rotations, i.e.,

$\angle W''X''Y''=82^\circ$

where, $\angle W'X"Y"$ is the image of $\angle WXY$ after the sequence of rotations.

Therefore, the size of the angle WXY after the sequence of rotations is 82°.

3 0

4 years ago

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The

Dmitry_Shevchenko [17]

Answer:

7 years

Step-by-step explanation:

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

6 0

4 years ago